In this paper, the attitude stability of liquid-filled spacecraft with flexible appendage is investigated. The motion of liquid sloshing is modeled as the spherical pendulum, and the flexible appendage is approached b...In this paper, the attitude stability of liquid-filled spacecraft with flexible appendage is investigated. The motion of liquid sloshing is modeled as the spherical pendulum, and the flexible appendage is approached by a linear shearing beam. Nonlinear dynamic equations of the coupled system are derived from the Hamiltonian. The stability of the coupled system was analyzed by using the energy-Casimir method, and the nonlinear stability theorem of the coupled spacecraft system was also obtained. Through numerical computation, the correctness of the proposed theorem is verified and the boundary curves of the stable region are presented. The increase of the angular velocity and flexible attachment length will weaken the attitude stability, and the change of the filled ratio of liquid fuel tank has a different influence on the stability of the coupled spacecraft, depending on the different conditions. The attitude stability analysis of the coupled spacecraft system in this context is useful for selecting appropriate parameters in the complex spacecraft design.展开更多
By employing the energy-Casimir method, a three-dimensional virtual pseudoenergy wave-activity relation for a moist atmosphere is derived from a complete system of nonhydrostatic equations in Cartesian coordinates. Si...By employing the energy-Casimir method, a three-dimensional virtual pseudoenergy wave-activity relation for a moist atmosphere is derived from a complete system of nonhydrostatic equations in Cartesian coordinates. Since this system of equations includes the effects of water substance, mass forcing, diabatic heating, and dissipations, the derived wave-activity relation generalizes the previous result for a dry atmosphere. The Casimir function used in the derivation is a monotonous function of virtual potential vorticity and virtual potential temperature. A virtual energy equation is employed （in place of the previous zonal momentum equation） in the derivation, and the basic state is stationary but can be three-dimensional or, at least, not necessarily zonally symmetric. The derived wave-activity relation is further used for the diagnosis of the evolution and propagation of meso-scale weather systems leading to heavy rainfall. Our diagnosis of two real eases of heavy precipitation shows that positive anomalies of the virtual pseudoenergy wave-activity density correspond well with the strong precipitation and are capable of indicating the movement of the precipitation region. This is largely due to the cyclonic vorticity perturbation and the vertically increasing virtual potential temperature over the precipitation region.展开更多
The stability of partly liquid filled spacecraft with flexible attachment was investigated in this paper. Liquid sloshing dynamics was simplified as the spring-mass model, and flexible attachment was modeled as the li...The stability of partly liquid filled spacecraft with flexible attachment was investigated in this paper. Liquid sloshing dynamics was simplified as the spring-mass model, and flexible attachment was modeled as the linear shearing beam. The dynamic equations and Hamiltonian of the coupled spacecraft system were given by analyzing the rigid body, liquid fuel, and flexible appendage. Nonlinear stability conditions of the coupled spacecraft system were derived by computing the variation of Casimir function which was added to the Hamiltonian. The stable region of the parameter space was given and validated by numerical computation. Related results suggest that the change of inertia matrix, the length of flexible attachment, spacecraft spinning rate, and filled ratio of liquid fuel tank have strong influence on the stability of the spacecraft system.展开更多
基金supported by the National Natural Science Foundation of China (Grants 11472041, 11532002)the Doctoral Fund of Ministry of Education of China (Grant 20131101110002)
文摘In this paper, the attitude stability of liquid-filled spacecraft with flexible appendage is investigated. The motion of liquid sloshing is modeled as the spherical pendulum, and the flexible appendage is approached by a linear shearing beam. Nonlinear dynamic equations of the coupled system are derived from the Hamiltonian. The stability of the coupled system was analyzed by using the energy-Casimir method, and the nonlinear stability theorem of the coupled spacecraft system was also obtained. Through numerical computation, the correctness of the proposed theorem is verified and the boundary curves of the stable region are presented. The increase of the angular velocity and flexible attachment length will weaken the attitude stability, and the change of the filled ratio of liquid fuel tank has a different influence on the stability of the coupled spacecraft, depending on the different conditions. The attitude stability analysis of the coupled spacecraft system in this context is useful for selecting appropriate parameters in the complex spacecraft design.
基金supported by the National Basic Research Program of China(Grant No.2013CB430105)the Key Program of the Chinese Academy of Sciences(Grant No.KZZD-EW-05)+1 种基金the National Natural Science Foundation of China(Grant No.41175060)the Project of CAMS,China(Grant No.2011LASW-B15)
文摘By employing the energy-Casimir method, a three-dimensional virtual pseudoenergy wave-activity relation for a moist atmosphere is derived from a complete system of nonhydrostatic equations in Cartesian coordinates. Since this system of equations includes the effects of water substance, mass forcing, diabatic heating, and dissipations, the derived wave-activity relation generalizes the previous result for a dry atmosphere. The Casimir function used in the derivation is a monotonous function of virtual potential vorticity and virtual potential temperature. A virtual energy equation is employed （in place of the previous zonal momentum equation） in the derivation, and the basic state is stationary but can be three-dimensional or, at least, not necessarily zonally symmetric. The derived wave-activity relation is further used for the diagnosis of the evolution and propagation of meso-scale weather systems leading to heavy rainfall. Our diagnosis of two real eases of heavy precipitation shows that positive anomalies of the virtual pseudoenergy wave-activity density correspond well with the strong precipitation and are capable of indicating the movement of the precipitation region. This is largely due to the cyclonic vorticity perturbation and the vertically increasing virtual potential temperature over the precipitation region.
基金supported by the National Natural Science Foundation of China (11472041, 11532002)the Innovation Fund Designated for Graduate Students of Beijing Institute of Technology (2015CX10003)the Research Fund for the Doctoral Program of Higher Education of China (20131101110002)
文摘The stability of partly liquid filled spacecraft with flexible attachment was investigated in this paper. Liquid sloshing dynamics was simplified as the spring-mass model, and flexible attachment was modeled as the linear shearing beam. The dynamic equations and Hamiltonian of the coupled spacecraft system were given by analyzing the rigid body, liquid fuel, and flexible appendage. Nonlinear stability conditions of the coupled spacecraft system were derived by computing the variation of Casimir function which was added to the Hamiltonian. The stable region of the parameter space was given and validated by numerical computation. Related results suggest that the change of inertia matrix, the length of flexible attachment, spacecraft spinning rate, and filled ratio of liquid fuel tank have strong influence on the stability of the spacecraft system.
